Layer List Widget (Beta) Button and Drop Down Menu Button not working

I know the Layer List Widget is still in Beta at v3.14, but I have been trying to add a Button (dijit.form.Button), or even better would be a Drop Down Menu Button (dijit.DropDownMenu) to the Layer List Widget via the button property. I can add the button and it shows up fine, but the click event is not firing, so the button is useless. I have tried using both a button and drop down menu button and tried using the LayerList button and content properties and both result in the same; the buttons show but do not work or fire the events. It almost seems like the events are blocked. It also seems like the button and content properties only support showing the parent node, no child nodes seem to display, so this could be related.

Has anyone successfully implemented buttons on the Layer List Widget? and if so how?

My scenario is a bit different as I am dynamically creating the layers for the layer list and thus dynamically creating the buttons programmatically in JavaScript not declaratively like your example. But your example does prove that the button property does work, so thanks for sharing. I have been able to add the sliders to the content property programmatically and added drop down menu buttons to the button property declaratively. Just not able to add the drop down buttons programmatically yet, they show but don't work, but it could be something I'm missing in my own code.

I was able to figure this out, it seems I have to do my dynamic creation of the button and popup menus and add to the layer List after the Layer List is loaded. If I do this prior to the Layer List load and pass in the UI gets messed up.

I am also trying to program a dropdown menu or radio button to toggle my layers. My problem with the default Layer List Widget is that I don't want users to open two layers at the same time due to poor map overlaying. The dropdown menu or radio button would limit users' access to only one layer at a time. Can you share some your code so I can learn from your wisdom?